\newpage

\chapter{Design of Networks}

\section{Rainfall station correlation} % (fold)
\input{./11/plot1.tikz} 
\\
The resulting fitting values for $d_0$ and $r_0$ are calculated as: \\
\\
\textbf{Monthly data} \\% (fold)
$d_0$ = 512.82km\\
$r_0$ = 0.97\\
\\
\textbf{Daily data} \\% (fold)
$d_0$ = 134.56\\
$r_0$ = 0.87\\

\subsection{Relative root mean square error} % (fold)

Using
\begin{equation}
{Z_{areal}} = \frac{{{\sigma _e}}}{{\bar P}} = {C_v} \cdot \sqrt {\left( {\frac{1}{N}(1 - {r_0} + \frac{{0.23}}{{{d_0}}}\sqrt {\frac{S}{N}} } \right)} 
\end{equation}
The relative root mean square error in areal rainfall estimate can be determined. \\
\\
For the example of Luxembourgh the relative root mean square error equals 6.9\%for daily measurements and 1.3\% for monthly measurements.

\subsection{Changing the equipment accuracy} % (fold)
By changing the equipment accuracy the 0.9 the error of the monthly measurements increase, whereas the error of the daily measurements decreases. This is illustrated in the graph below: \\
\input{./11/plot2.tikz} \\
The amount of rain gauges needed to gain the same Zareal for daily measurements is 7.
\subsection{Changes in coefficient in variation and characteristic correlation} % (fold)
To maintain the same relative error 11 stations will have to be operated during daily measurements with increased variation coefficients. The impact of changes in the characteristic correlation ($d_0$) is negligible. \\
\\
\input{./11/plot3.tikz} 

\subsection{Exceedence Calculation} % (fold)
\input{./11/plot4.tikz}

